Is it possible to blend a tiled texture with itself?
I will assume you want to blend a planar tiling. Not to blend a cube mapping between sides.

If you really want to then yes its possible, but it is much more complicated than doing it in some 2D app.

For the blending to work, the tiles need to overlap. You can manipulate the tiling with mapping vectors no problem: How do I create repeating patterns with cycles&#39; procedural textures

What the problem is is to map two source mapping locations into 1 output location for the blending. That would require a function that gives 2 values for 1 input >> impossible.

The workaround would be to use 2 textures, each tiled like chessboard colors. The tilling would overlap between the two and you could mix them with linear weights of how far from the tilling border the pixel is. This would still cause artifacts on tile corners when blended both in X and Y so 3 textures would be actually ideal.

And the blending would look not good at all, I think you are better to make a tileable texture with clone brush, because this is not worth it.